Optimal. Leaf size=25 \[ \text {Int}\left (\frac {(e (c+d x))^m}{a+b \sin ^{-1}(c+d x)},x\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \frac {(c e+d e x)^m}{a+b \sin ^{-1}(c+d x)} \, dx \]
Verification is Not applicable to the result.
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Rubi steps
\begin {align*} \int \frac {(c e+d e x)^m}{a+b \sin ^{-1}(c+d x)} \, dx &=\frac {\operatorname {Subst}\left (\int \frac {(e x)^m}{a+b \sin ^{-1}(x)} \, dx,x,c+d x\right )}{d}\\ \end {align*}
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Mathematica [A] time = 1.60, size = 0, normalized size = 0.00 \[ \int \frac {(c e+d e x)^m}{a+b \sin ^{-1}(c+d x)} \, dx \]
Verification is Not applicable to the result.
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fricas [A] time = 0.54, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\frac {{\left (d e x + c e\right )}^{m}}{b \arcsin \left (d x + c\right ) + a}, x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (d e x + c e\right )}^{m}}{b \arcsin \left (d x + c\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 1.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (d e x +c e \right )^{m}}{a +b \arcsin \left (d x +c \right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {{\left (d e x + c e\right )}^{m}}{b \arcsin \left (d x + c\right ) + a}\,{d x} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [A] time = 0.00, size = -1, normalized size = -0.04 \[ \int \frac {{\left (c\,e+d\,e\,x\right )}^m}{a+b\,\mathrm {asin}\left (c+d\,x\right )} \,d x \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {\left (e \left (c + d x\right )\right )^{m}}{a + b \operatorname {asin}{\left (c + d x \right )}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
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